We have seen that all vector fields of the form F = ∇g satisfy the equation curl F = 0 and that all vector fields of the form F = curl G satisfy the equation div F = 0 (assuming continuity of the appropriate partial derivatives). This suggests the question: are there any equations that all functions of the form f = div G must satisfy? Show that the answer to this question is “No” by proving that every continuous function f on R³ is the divergence of some vector field.